ERROR
Vak Dated 12.Oct. 2019
There was a minor error in the frequency up-shift equations which was found while cross checking NUMERICALLY while using EXCEL worksheets
Now it is corrected.
This error appeared in the exact calculation of Initial frequency and final frequency at the time of BENDING of Electro-magnetic ray / light ray near Gravitational mass.
Hence all the published papers papers stand corrected as given below....
Case3. When the velocity of gravitational mass is
not exactly opposite or exactly in the same direction to the incoming light
ray:
In this case the gravitational field will act as some brake or enhance
the energy of the incoming light ray depending on (Cos ϕ) of the
velocity of gravitational mass relative to incoming radiation, where (ϕ)
is the angle between the light ray and velocity of gravitational mass .
The gravitating mass is moving with a velocity μ making
an angle (ϕ) as the angle between light ray velocity of gravitating
mass and applies brake on the photon. This is something similar to the case
where the gravitational mass is fixed in position and the photon of the rest
mass E / c2 is
moving with velocity μ Cos ϕ +c
Hence the initial velocity of photon = - μ Cos ϕ -c. It’s velocity is
towards the gravitational mass. The photon is having a freefall. Its final velocity = - μ Cos ϕ -c - got
[ where t is the time of flight of photon].
Initial Energy = m (μ Cos ϕ +c)2 /2
= E (μ Cos ϕ +c)2 /2 c2 = E (μ2
Cos2 ϕ +c2+2μ Cos ϕ c )/2c2
Initial Frequency = ϑi =1/ [ m (μ Cos ϕ +c)2
/2 ]
=1/ [ E (μ Cos
ϕ +c)2 /2 c2 = E (μ2 Cos2
ϕ +c2+2μ Cos ϕ c ) ]
here E = h ϑ that
means
= ϑi = 1/{ h (μ2 Cos2 ϕ
+c2+2μ Cos ϕ c )/2c2 }
= { 2c2
/h (μ2 Cos2 ϕ +c2+2μ
Cos ϕ c )}
6.0.1. From excel
sheet Derivation of equations for the effect of movement of gravitational
mass on the frequency of the incoming light ray with c:
Energy due to Gravitation of Sun (or star) on the photon =
Es =
Initial Energy = m (μ Cos ϕ +c)2
/2 = E (μ Cos ϕ +c)2 /2 c2 =
E (μ2 Cos2 ϕ +c2+2μ Cos
ϕ c )/2c2
Frequency
of photon = ϑ = E /
h or E = h ϑ
Energy due to Gravitation of Sun
(or star) on the photon = Es = E go r /c2
= Initial Energy = m (μ Cos ϕ +c)2
/2 vak 12102019 ?????
Initial Frequency = ϑi =1/ [ m (μ Cos ϕ +c)2
/2 ] wrong 12102019
= E (μ2 Cos2
ϕ +c2+2μ Cos ϕ c )/2hc2
= E (μ Cos
ϕ +c)2 /2 hc2
Vak 18DEC 2019: ERRATA
The above equations which are in red colour in strikeout format were wrong. This
mistake happened while reducing the equation to derive “Initial Frequency = ϑi” and “Final
Frequency = ϑo”. This was found while doing calculations
numerically in excel. There was a result mismatch.
Now the error was corrected.
Sorry for the error, and the Author regrets the
error
=snp.gupta 18DEC 2019
